Objective: Students will be able to identify a division word problem as either sharing or grouping and communicate their reasoning.

Big Idea:
Division is a complex task for children of this age. Realizing what information a word problem supplies and what needs to be found is fundamental and challenging. This lesson begins that challenge.

Today I want to see if my students are able to decipher between the two types of dividing. Working with the CCSS has led me to understand that children need to know this difference in order to understand what they are solving for in a division problem. No longer is it okay for me to just see if they can solve for the right number. Students are expected to explain their reasoning, and so they must understand/ communicate what they are solving for (a group size, or a number of groups)

To begin my mini lesson, I remind the students of some lesson activities that we've done (described below). Then, I ask them to watch the following two clips. Even though the word "sharing" is on the first video, I want them to name what type of division it is and why.

We have worked on various activities where the students divided by sharing and also by grouping. One of the main activities for sharing was our work with "The Doorbell Rang" by Pat Hutchins. In those lessons, the students passed out "cookies" to a certain number of people until they were all out.

To work on the grouping model, we created a cookie production company and the students had to create packages of cookies. We also worked on a marching band project which asked them to configure a band for a parade.

This is such a sweet little clip. It doesn't show the kids sharing with more than one other, but the context of sharing is obvious. (Passing out one at a time from the whole.) Stop the video before the information on hunger if you choose.

I used a video clip of a marching band in another lesson and the students loved it. It is okay to have some fun while showing real world use of a concept. Can you imagine all of the division to make this band show work? If you choose to use this lesson, find your own alma mater or your local high school on YouTube and let the kids enjoy real math.

This next video is a bit long, so I fast forward to the part when the band begins playing and grouping (about 2:30 in). Seeing the band come onto the field can also be interesting, as it comes out in sets.

After watching the clips, discuss WHY they show each type of sharing, rather than labeling the types of division.

For the student practice, I've created several Division Stories that are examples of sharing or grouping division problems. I ask the students to create a 3 by 3 grid in their notebooks and write either "sharing" or "grouping" in each box for a tic tac toe game.

I then read the cards and have them put a marker in a box that describes the cards I read. Obviously, the round ends when someone has tic tac toe. I will have the cards on the board for everyone to see and the "winner" must come up and explain his/her answer. In order to be successful and declare the "win", reasoning must be applied by the student. He or she will need to explain why the stories were sharing or grouping. They may choose to just talk it out or draw a model on the board. The group can disagree if needed!

Resources

For independent work, I pass out six stories to the students. They must decide if they are sharing or grouping problems and glue them onto an organizer I downloaded from K-5 Math Teaching Resources.

After they sort they are to solve the problem and show their work. I add to this student work and suggest you also do so. Students are expected to also write at the bottom of the page how they know it was sharing or grouping.

If this lesson is longer than your session allows, doing a couple of these in class and then the rest for practice at home is a nice balance.

This team is trying to put language to their understanding…a complicated thing for a child still developing language (8 and 9 years old). If you really listen, you can hear that they know what they are talking about.

This partnership struggled. They were debating when I approached, but began to agree when I hit record. They are able to respectfully agree and disagree and explain their thinking.